JEE Mains · Maths · STD 11 - 6. permutation and combination
Eight persons are to be transported from city \(A\) to city \(B\) in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is \(...........\).
- A \(3360\)
- B \(1680\)
- C \(560\)
- D \(1120\)
Answer & Solution
Correct Answer
(B) \(1680\)
Step-by-step Solution
Detailed explanation
\(\text { Ways }=\frac{8 !}{3 ! 3 ! 2 ! 2 !} \times 3 !\) \(=\frac{8 \times 7 \times 6 \times 5 \times 4}{4}\) \(=56 \times 30\) \(=1680\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(S=\left\{(x, y) \in N \times N : 9(x-3)^{2}+16(y-4)^{2} \leq 144\right\}\) and \( T=\left\{(x, y) \in R \times R :(x-7)^{2}+(y-4)^{2} \leq 36\right\}\) Then \(n ( S \cap T )\) is equal to \(......\)JEE Mains 2022 Hard
- Let the domain of the function
\(f(x)=\cos ^{-1}\left(\frac{4 x+5}{3 x-7}\right)\) be \([\alpha, \beta]\) and the domain of \(\mathrm{g}(\mathrm{x})=\log _2\left(2-6 \log _{27}(2 \mathrm{x}+5)\right)\) be \((\gamma, \delta)\).
Then \(|7(\alpha+\beta)+4(\gamma+\delta)|\) is equal to ________JEE Mains 2025 Medium - Let the plane \(2 x+3 y+z+20=0\) be rotated through a right angle about its line of intersection with the plane \(x-3 y+5 z=8\). If the mirror image of the point \(\left(2,-\frac{1}{2}, 2\right)\) in the rotated plane is \(B ( a , b , c )\), thenJEE Mains 2022 Hard
- Let \(\hat{a}, \hat{b}\) be unit vectors. If \(\vec{c}\) be a vector such that the angle between \(\hat{ a }\) and \(\overrightarrow{ c }\) is \(\frac{\pi}{12}\), and \(\hat{ b }=\overrightarrow{ c }+2(\overrightarrow{ c } \times \hat{ a })\), then \(|6 \overrightarrow{ c }|^{2}\) is equal toJEE Mains 2022 Hard
- Let \(x=x(y)\) be the solution of the differential equation \(y^2 \mathrm{~d} x+\left(x-\frac{1}{y}\right) \mathrm{d} y=0\). If \(x(1)=1\), then \(x\left(\frac{1}{2}\right)\) is :JEE Mains 2025 Hard
- If \(a=\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{2 n}{n^{2}+k^{2}}\) and \(f(x)=\) \(\sqrt{\frac{1-\cos x}{1+\cos x}}, x \in(0,1)\), then.JEE Mains 2022 Hard
More PYQs from JEE Mains
- Let \(p , q \in R\) and \((1-\sqrt{3} i )^{200}=2^{199}( p + iq )\), \(i =\sqrt{-1}\) Then \(p + q + q ^2\) and \(p - q + q ^2\) are roots of the equation.JEE Mains 2023 Hard
- Let \(A=\left[a_{i j}\right], a_{i j} \in Z \cap[0,4], 1 \leq i, j \leq 2\). The number of matrices \(A\) such that the sum of all entries is a prime number \(p \in(2,13)\) is \(........\).JEE Mains 2023 Hard
- Let \(f\) be a differential function such that \(f'\left( x \right) = 7 - \frac{3}{4}\frac{{f\left( x \right)}}{x},\left( {x > 0} \right)\) and \(f(1) \ne 4\). Then \(\mathop {\lim }\limits_{x \to {0^ + }} xf\left( {\frac{1}{x}} \right)\)JEE Mains 2019 Hard
- Number of \(4-\)digit numbers (the repetition of digits is allowed) which are made using the digits \(1, 2, 3\) and \(5\) , and are divisible by \(15\) , is equal to \(............\).JEE Mains 2023 Hard
- Let the focal chord \(P Q\) of the parabola \(y^2=4 x\) make an angle of \(60^{\circ}\) with the positive \(x\)-axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the \(y\)-axis at the point \((0, \alpha)\), then \(5 \alpha^2\) is equal to :JEE Mains 2025 Easy
- The mean of the data set comprising of \(16\) observations is \(16.\) If one of the observation valued \(16\) is deleted and three new observations valued \(3, 4\) and \(5\) are added to the data, then the mean of the resultant data, is:JEE Mains 2015 Medium